# Investigation on the Mechanical Behavior of Paper and Paper Stacks in the out-of-plane Direction

## Abstract

The purpose of the present study is to deeply investigate the mechanical behavior of paper materials in the out-of-plane direction, especially, the compressive behavior of a single sheet or multiple sheets. In this dissertation, the mechanical behavior of paper and paper stacks was detailed discussed from three different research perspectives. The surface roughness plays a very important role in the compressive behavior of paper materials. The first goal of the present study is to investigate the effect of the surface topography in calculating the stress-strain curve of paper. The difference between the actual and the nominal contact area was compared and a new experimental method by using carbon papers was proposed to measure the actual contact areas. With the aid of the image processing technology, the actual stress-strain curve of paper was calculated and compared with the nominal stress-strain curve. As indicated, there is an obvious difference between the actual and nominal stress-strain curves. A second goal of this study is to establish the mathematical model for describing the force-deformation behavior of multiple sheets. Two different methods with and without considering the paper structures were selected for building the paper models. With considering the structure, the paper can be regarded as an elastic material, the body of which can be divided into two rough surfaces and one internal structure. On the basis of Hooke’s law or Paetow’s method, the relationship between the total deformation and surface deformation can be calculated by using the Newton-Raphson method. Then, the force-deformation relation of a single sheet was derived according to the relationship between the surface and total deformation, the model of a single sheet was extended to calculate the force-deformation curves of multiple sheets. Without considering the structure, the loading and unloading stress-strain curve of paper were expressed by using a sextic polynomial equation and a modified exponential equation, respectively. Based on the hypothesis that when the force is the same, the deformations of the paper stacks are directly proportional to the sheet numbers, the force-deformation relation of multiple sheets was derived. By comparing with the experimental results, it shows that the maximum number of sheets which can be calculated by both of the proposed models is about 140 sheets, especially, when the numbers are between 20 and 140. In addition, without considering the effect of the surface roughness, the stress-strain curve of paper is a typical J-shaped curve. So, in this dissertation, a much easier way to simulate the paper material by using a gasket model was proposed. The material property was defined based on the experimental stress-deformation data under 100 N, then, some simulations under 20 N, 40 N, 60 N and 80 N were implemented based on the model established above. The findings indicated that, this method can be used with high confidence for the simulation of paper under different forces.

Item Type: Ph.D. Thesis
Erschienen: 2016
Creators: Chen, Jian
Title: Investigation on the Mechanical Behavior of Paper and Paper Stacks in the out-of-plane Direction
Language: English
Abstract:

The purpose of the present study is to deeply investigate the mechanical behavior of paper materials in the out-of-plane direction, especially, the compressive behavior of a single sheet or multiple sheets. In this dissertation, the mechanical behavior of paper and paper stacks was detailed discussed from three different research perspectives. The surface roughness plays a very important role in the compressive behavior of paper materials. The first goal of the present study is to investigate the effect of the surface topography in calculating the stress-strain curve of paper. The difference between the actual and the nominal contact area was compared and a new experimental method by using carbon papers was proposed to measure the actual contact areas. With the aid of the image processing technology, the actual stress-strain curve of paper was calculated and compared with the nominal stress-strain curve. As indicated, there is an obvious difference between the actual and nominal stress-strain curves. A second goal of this study is to establish the mathematical model for describing the force-deformation behavior of multiple sheets. Two different methods with and without considering the paper structures were selected for building the paper models. With considering the structure, the paper can be regarded as an elastic material, the body of which can be divided into two rough surfaces and one internal structure. On the basis of Hooke’s law or Paetow’s method, the relationship between the total deformation and surface deformation can be calculated by using the Newton-Raphson method. Then, the force-deformation relation of a single sheet was derived according to the relationship between the surface and total deformation, the model of a single sheet was extended to calculate the force-deformation curves of multiple sheets. Without considering the structure, the loading and unloading stress-strain curve of paper were expressed by using a sextic polynomial equation and a modified exponential equation, respectively. Based on the hypothesis that when the force is the same, the deformations of the paper stacks are directly proportional to the sheet numbers, the force-deformation relation of multiple sheets was derived. By comparing with the experimental results, it shows that the maximum number of sheets which can be calculated by both of the proposed models is about 140 sheets, especially, when the numbers are between 20 and 140. In addition, without considering the effect of the surface roughness, the stress-strain curve of paper is a typical J-shaped curve. So, in this dissertation, a much easier way to simulate the paper material by using a gasket model was proposed. The material property was defined based on the experimental stress-deformation data under 100 N, then, some simulations under 20 N, 40 N, 60 N and 80 N were implemented based on the model established above. The findings indicated that, this method can be used with high confidence for the simulation of paper under different forces.

Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Institute of Printing Science and Technology (IDD)
Date Deposited: 20 Nov 2016 20:55
URN: urn:nbn:de:tuda-tuprints-57709
Referees: Dörsam, Prof. Edgar ; Schabel, Prof. Samuel
Refereed / Verteidigung / mdl. Prüfung: 1 November 2016
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Das Ziel der vorliegenden Arbeit ist das mechanische Verhalten von Papiermaterialien in z-Richtung genauestens zu untersuchen, insbesondere das Pressverhalten von einem einzelnen Blatt oder mehreren Blättern. In dieser Arbeit wurde das mechanische Verhalten von Papier und Papierstapel aus drei unterschiedlichen Forschungsperspektiven detailliert diskutiert. Die Oberflächenrauigkeit spielt beim Pressverhalten von Papiermaterialien eine sehr wichtige Rolle. Das erste Ziel der vorliegenden Arbeit ist es der Wirkung der Oberflächentopographie bei der Berechnung der Spannungs-Dehnungs-Kurve des Papiers zu untersuchen. Verglichen wurde die Differenz zwischen der tatsächlichen Kontaktfläche und der Nennkontaktfläche. Des Weiteren wurde eine neue experimentelle Methode vorgeschlagen, bei dem Kohlepapier angewandt wird um die tatsächlichen Kontaktfläche zu messen. Mit Hilfe der Bildverarbeitungstechnik wird die tatsächliche Spannungs-Dehnungskurve des Papiers berechnet und mit der Nennspannungs-Dehnungskurve verglichen. Wie schon angedeutet, besteht zwischen den Ist- und Soll-Spannungs-Dehnungs-Kurven eine offensichtliche Differenz. Ein weiteres Ziel dieser Arbeit ist das mathematische Modell zur Beschreibung des Kraft-Verformungsverhalten von mehreren Blättern zu etablieren. Zwei verschiedene Methoden, mit und ohne Berücksichtigung der Papierstrukturen, werden für den Aufbau der Papiermodelle ausgewählt. Unter Berücksichtigung der Papierstruktur, kann das Papier als elastisches Material angesehen werden, dessen Körper in zwei raue Oberflächen und einer inneren Struktur unterteilt wird. Auf der Grundlage des Hookschen Gesetzes oder der Paetow Methode kann die Beziehung zwischen der Gesamtverformung und Oberflächenverformung durch Verwendung der Newton-Raphson-Methode berechnet werden. Dann wurde das Kraft-Verformungsverhalten der einzelnen Blätter abgeleitet und entsprechende Beziehungen zwischen der Oberfläche und der Gesamtverformung, das Modell des einzelnen Blattes wird erweitert, um weiterhin die Kraft-Verformungskurven von mehreren Blättern berechnen zu können. Ohne Berücksichtigung der Papierstruktur wird die Be- und Entlastung der Spannungs-Dehnungs-Kurve des Papiers jeweils durch eine Sextik Polynomgleichung und eine modifizierte exponentielle Gleichung ausgedrückt. Basierend auf der Hypothese, dass unter gleicher Kraft die Verformungen der Papierstapel direkt proportional zu den Blattnummern sind, wird die Kraft-Verformungs-Beziehung von mehreren Blättern abgeleitet. Durch den Vergleich mit den experimentellen Ergebnissen zeigt sich, dass die maximale Anzahl von Blättern, die von beiden der vorgeschlagenen Modelle, mit etwa 140 Blatt berechnet werden kann. Darüber hinaus, ohne dabei den Effekt der Oberflächenrauigkeit zu berücksichtigen, ist die Spannungs-Dehnungs-Kurve des Papiers eine typische J-förmige Kurve. In dieser Arbeit wird ein viel einfacherer Weg vorgeschlagen, um das Papiermaterial durch die Verwendung eines Dichtungs Modell zu simulieren. Die Materialeigenschaft wurde auf Grundlage der Daten des experimentellen Druckverschlusses unter 100 N definiert, dann wurden einige Simulationen unter 20 N, 40 N, 60 N und 80 N basierend auf dem oben etabliert Modell umgesetzt. Aus den Ergebnissen zeigt sich, dass dieses Verfahren mit hoher Wahrscheinlichkeit für die Simulation von Papier unter verschiedenen Kräften verwendet werden kann.

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